Rollout Algorithms for Stochastic Scheduling Problems

Stochastic scheduling problems are difficult stochastic control problems with combinatorial decision spaces. In this paper we focus on a class of stochastic scheduling problems, the quiz problem and its variations. We discuss the use of heuristics for their solution, and we propose rollout algorithms based on these heuristics, which approximate the stochastic dynamic programming algorithm. We show how the rollout algorithms can be implemented efficiently, and we delineate circumstances under which they are guaranteed to perform better than the heuristics on which they are based. We also show computational results which suggest that the performance of the rollout policies is near-optimal, and is substantially better than the performance of their underlying heuristics. 1 This work was supported in part by the Air Force Office of Scientific Research under grant no. F49620-97-C-0013 2 Department of Electrical Engineering and Computer Science, M. I. T., Cambridge, Mass., 02139. 3 Department of Electrical Engineering, Boston University, and ALPHATECH, Inc., Burlington, Mass., 01803.